Theoretical investigations of Ge1-x Sn x alloys (x=0, 0.333, 0.667, 1) in P42/ncm phase

The structural, mechanical, anisotropic and electronic properties of Ge, Sn and their alloys (Ge0.667Sn0.333 and Ge0.333Sn0.667) in P4(2)/ncm phase were studied in the framework of the density functional theory. In the present work, the lattice parameters increase with the increased tin concentration, whereas the elastic constants and elastic modulus of Ge1-x Sn (x) alloys (x = 0, 0.333, 0.667, 1) in P4(2)/ncm phase decrease with the increased tin concentration. A novel Sn allotrope with remarkable stability (the energy is higher than Sn in diamond phase only 24.4 meV per atom) in P4(2)/ncm phase is first proposed in the present work, and it is a quasi-direct band gap semiconductor material with bang gap of 1.02 eV. The dynamically, mechanically and thermodynamically stable forms of P4(2)/ncm-Sn and the Ge-Sn alloys in P4(2)/ncm phase are proved by phonon spectra, elastic constants, formation enthalpy and cohesive energies. The universal elastic anisotropy index A (U) illustrates that the anisotropy of Ge1-x Sn (x) alloys (x = 0, 0.333, 0.667, 1) in P4(2)/ncm phase increases with the increasing percentage of the tin composition. To obtain the details of the anisotropy, the Young's modulus, bulk modulus, shear modulus and Poisson's ratio are also systematically investigated. The electronic band structures of Ge1-x Sn (x) alloys (x = 0, 0.333) in P4(2)/ncm phase with HSE06 hybrid functional show that both of them are indirect band gap semiconductors, while Ge0.333Sn0.667 and Sn in the P4(2)/ncm phase show that they are quasi-direct band gap semiconductor materials.